Stephan Hartmann

Here P is the density operator of the system under consideration, and σ ± and σ 3 are the usual Pauli matrices, acting on atom i whose states are |1 > or |0 >, representing, respectively, the atom being in an excited state or in the ground state. B and C are appropriate decay constants and s has been called the pumping parameter [1]. It varies from s = 0 for pure damping to s = 1 for full laser action. To solve the corresponding quantum master equations, three approaches have been taken: First, one focuses on the case of one atom. Second, one truncates eq. (1) and derives semi-classical models. Third, one employs numerical simulation methods such as the quantum trajectory method. While the latter method is very popular, it should be noted that the numerical complexity of the problem increases exponentially with the number of atoms, and so numerical methods soon become unfeasible.

Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much—perhaps most—of what we believe through the testimony of others, the simple matter of acquiring conditionals via others’ assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning – a challenge which no account presently fully meets.

This volume, the third in this Springer series, contains selected papers from the four workshops organized by the ESF Research Networking Programme "The Philosophy of Science in a European Perspective" (PSE) in 2010: Pluralism in the Foundations of Statistics Points of Contact between the Philosophy of Physics and the Philosophy of Biology The Debate on Mathematical Modeling in the Social Sciences Historical Debates about Logic, Probability and Statistics The volume is accordingly divided in four sections, each of them containing papers coming from the workshop focussing on one of these themes. While the programme's core topic for the year 2010 was probability and statistics, the organizers of the workshops embraced the opportunity of building bridges to more or less closely connected issues in general philosophy of science, philosophy of physics and philosophy of the special sciences. However, papers that analyze the concept of probability for various philosophical purposes are clearly a major theme in this volume, as it was in the previous volumes of the same series. This reflects the impressive productivity of probabilistic approaches in the philosophy of science, which form an important part of what has become known as formal epistemology - although, of course, there are non-probabilistic approaches in formal epistemology as well. It is probably fair to say that Europe has been particularly strong in this area of philosophy in recent years.​

Equal and proportional representation are two poles of a continuum of models of representation for the assembly of a federation of states. The choice of a model has repercussions on the welfare distribution in the federation. We determine, first by means of Monte Carlo simulations, what welfare distributions result after assemblies that were constituted on the basis of different models of representation have considered a large number of motions. We assess what model of representation is favored by a Rawlsian maximin measure and by the utilitarian measure and present matching analytical results for the utilitarian measure for a slightly idealized case. Our results show that degressive proportionality can be justified as a compromise between maximin and utilitarian considerations. There is little surprise in this result. What is more surprising, however, is that, within certain contexts of evaluation, degressive proportionality can also be justified on strictly utilitarian grounds

Bonjour (1985: 101 and 1999: 124) and other coherence theorists of justification before him (e.g. Ewing, 1934: 246) have complained that we do not have a satisfactory analysis of the notion of coherence. The problem with existing accounts of coherence is that they try to bring precision to our intuitive notion of coherence independently of the particular role that it is meant to play within the coherence theory of justification (e.g Lewis, 1946: 338). This is a mistake: it does not make any sense to ask what precisely makes for a more coherent information set independently of the particular role that coherence is supposed to play within the context in question. What is this context and what is this role? The coherence theory of justification rides on a particular common sense intuition: when we gather information from less than fully reliable sources, then the more coherent the story that materializes is, the more confident we may be, ceteris paribus. Within the context of information gathering from certain types of sources, coherence is a property of stories which plays a confidence boosting role. But what features should the information sources have, so that the coherence of the information set is indeed a determinant of our degree of confidence in question? And what goes into the ceteris paribus clause? In other words, what other factors affect our confidence in the information set in question?

A conjunction of two hypotheses may provide a better explanation than either one of them individually, even if each already provides a good explanation on its own. An appropriate measure of explanatory power should reflect this, but none of the measures discussed in the literature do so because they only consider how much an explanatory hypothesis reduces our surprise at the evidence – which is problematic. This chapter introduces and defends a class of coherentist measures of explanatory power, and shows that one particular such measure that combines different intuitions underlying the epistemological notion of coherence overcomes the aforementioned problems of surprise reduction measures.

Philosophy, perhaps more than any other academic discipline, likes to reflect upon itself. Thus, it is no surprise that philosophers regularly ask questions such as: What is the scope of philosophy, what are its important questions, and what are the proper methods to address them? Asking these questions also means to take stock and to enquire where the discipline is going. This is an especially worthwhile activity in contemporary philosophy of science as this field has been changing rapidly since its institutional consolidation in the 1950s. For present purposes we may very roughly, but still usefully, describe this change as having three phases. In the first phase, which lasted until the mid 1960s, philosophy of science was dominated by Logical Empiricism and formal approaches to philosophically analyzing science. The second phase began in the late 1960s and lasted until the second half of the 1980s. It brought the naturalistic turn, a critique of the Logical Empiricist’s picture of science as too far away from the actual practice of science, a focus on the history and the social structure of science, a shift from theories as the primary target of philosophical analysis to models and experimental practices, and many detailed case studies. While the Logical Empiricists gave us a grand general picture of science, the naturalists’ working assumption has been that aiming at such a picture underappreciates the complexity and diversity of real science. Moreover, the naturalists moved normative questions into the background. In the third phase, which began in the late 1980s, the dichotomy between normative and descriptive approaches in philosophy of science still persists, but the picture has become even more complex. So we can only list a number of novel trends: Metaphysical questions, which were famously dismissed by the Logical Empiricists, are gaining a considerable interest. Philosophies of the special sciences are booming, and more and more subdisciplines are emerging. Formal epistemologists are applying a variety of mathematical methods to address normative questions in general philosophy of science. Social aspects of science are systematically studied and mathematically modeled. Another interesting development is the rise of experimental approaches to problems from philosophy of science (e.g., causation) and its combination with formal approaches. This (incomplete) list shows that contemporary philosophers of science address a large variety of topics. They also use many different methods, quite similar to scientists who often use a combination of methods, or import a method from another field to solve their problems. This is, to our mind, a fruitful way of conducting “scientific philosophy”: a proper combination of conceptual analysis, historical or contemporary case studies, formal modeling, and experimental work that will lead to many new and exciting insights.

Science presents us with a variety of accounts of the world. While some of these accounts posit deep theoretical structure and fundamental entities, others do not. But which of these approaches is the right one? How should science conceptualize the world? And what is the relation between the various accounts? Opinions on these issues diverge wildly in philosophy of science. At one extreme are reductionists who argue that higher-level theories should, in principle, be incorporated in, or eliminated by, the basic-level theory. According to this view, higher-level theories do not ultimately exhibit conceptual integrity or provide genuine explanations. At the other extreme are pluralists who take higher levels of description and explanation seriously and argue for their independence and indispensability. It was the aim of the first Sydney–Tilburg conference on “Reduction and the Special Sciences”, which took place at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in Tilburg, The Netherlands, over the 10–12th April 2008, to bring researchers working on these questions together and provide a platform to discuss them in a focused way. The papers in this special issue were presented at this conference. We would like to thank the Royal Netherlands Academy of Art and Sciences (KNAW), the Sydney Centre for the Foundations of Science at the University of Sydney and TiLPS for financial and institutional support. We also thank the authors and referees of the papers for their work, and Hans Rott for his support of this project.

This volume, the second in the Springer series Philosophy of Science in a European Perspective, contains selected papers from the workshops organised by the ESF Research Networking Programme PSE (The Philosophy of Science in a European Perspective) in 2009. Five general topics are addressed: 1. Formal Methods in the Philosophy of Science; 2. Philosophy of the Natural and Life Sciences; 3. Philosophy of the Cultural and Social Sciences; 4. Philosophy of the Physical Sciences; 5. History of the Philosophy of Science. This volume is accordingly divided in five sections, each section containing papers coming from the meetings focussing on one of these five themes. However, these sections are not completely independent and detached from each other. For example, an important connecting thread running through a substantial number of papers in this volume is the concept of probability: probability plays a central role in present-day discussions in formal epistemology, in the philosophy of the physical sciences, and in general methodological debates---it is central in discussions concerning explanation, prediction and confirmation. The volume thus also attempts to represent the intellectual exchange between the various fields in the philosophy of science that was central in the ESF workshops.

The roles models play in science have long been recognised and sparked rich and varied philosophical debates. In recent years attention has also been paid to the computational techniques used in the sciences, and the question arose what the implications were of the use of computer simulations for our understanding of scientific modelling, and science more generally. This was the subject of the conference “Models and Simulations”, which took place at the IHPST in Paris in June 2006. Selected papers of that conference appeared in a special issue of this journal (Synthese 169(3) (2009)). After the conference there was a general feeling that there still was much ground to cover, and so we decided to organize a follow up a year later. “Models and Simulations 2” took place in October 2007 at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in the Netherlands. The conference was made possible due to generous financial support from IHPST (Paris, CNRS), Universitat de Barcelona, TiLPS (Tilburg Center for Logic and Philosophy of Science) and the Evert Willem Beth Foundation. The papers in this special issue were presented at the conference and selected after a double-blind review process. We would like to thank the authors and referees of the papers for their work, and Vincent Hendricks and John Symons for their support of the project of another special issue on models and simulations.

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.

This volume, the third in this Springer series, contains selected papers from the four workshops organized by the ESF Research Networking Programme "The Philosophy of Science in a European Perspective" in 2010: Pluralism in the Foundations of Statistics Points of Contact between the Philosophy of Physics and the Philosophy of Biology The Debate on Mathematical Modeling in the Social Sciences Historical Debates about Logic, Probability and Statistics The volume is accordingly divided in four sections, each of them containing papers coming from the workshop focussing on one of these themes. While the programme's core topic for the year 2010 was probability and statistics, the organizers of the workshops embraced the opportunity of building bridges to more or less closely connected issues in general philosophy of science, philosophy of physics and philosophy of the special sciences. However, papers that analyze the concept of probability for various philosophical purposes are clearly a major theme in this volume, as it was in the previous volumes of the same series. This reflects the impressive productivity of probabilistic approaches in the philosophy of science, which form an important part of what has become known as formal epistemology - although, of course, there are non-probabilistic approaches in formal epistemology as well. It is probably fair to say that Europe has been particularly strong in this area of philosophy in recent years.​

Wann ist Kohärenz ein Indiz für Wahrheit? Können Informationsmengen immer entsprechend ihrer Kohärenz geordnet werden? Welche Rolle spielt Kohärenz bei der Theoriewahl in der Wissenschaft? Unter welchen Umständen kann eine wissenschaftliche Theorie mit nur teilweise zuverlässigen Messinstrumenten bestätigt werden? Ist die Belegvielfaltsthese wahr? Warum sind übereinstimmende Aussagen unabhängiger Zeugen so gewichtig? Dies sind einige der Fragen, die in diesem Buch in einem wahrscheinlichkeitstheoretischen Kontext und auf der Grundlage konkreter Modelle behandelt werden. Darüber hinaus bietet das Buch eine elementare Einführung in die Theorie der Bayesianischen Netzwerke und zeigt Verbindungen auf zu Debatten in der Kognitionswissenschaft (Tversky und Kahnemans Linda Problem), Sozialwahltheorie (Condorcet Jury Theorem) und Informatik (Repräsentation von Glaubenssystemen). Das Buch richtet sich an alle, die sich für die Anwendung wahrscheinlichkeitstheoretischer Methoden in der Philosophie interessieren.

Many results of modern physics—those of quantum mechanics, for instance—come in a probabilistic guise. But what do probabilistic statements in physics mean? Are probabilities matters of objective fact and part of the furniture of the world, as objectivists think? Or do they only express ignorance or belief, as Bayesians suggest? And how are probabilistic hypotheses justified and supported by empirical evidence? Finally, what does the probabilistic nature of physics imply for our understanding of the world? This volume is the first to provide a philosophical appraisal of probabilities in all of physics. Its main aim is to make sense of probabilistic statements as they occur in the various physical theories and models and to provide a plausible epistemology and metaphysics of probabilities. The essays collected here consider statistical physics, probabilistic modelling, and quantum mechanics, and critically assess the merits and disadvantages of objectivist and subjectivist views of probabilities in these fields. In particular, the Bayesian and Humean views of probabilities and the varieties of Boltzmann's typicality approach are examined. The contributions on quantum mechanics discuss the special character of quantum correlations, the justification of the famous Born Rule, and the role of probabilities in a quantum field theoretic framework. Finally, the connections between probabilities and foundational issues in physics are explored. The Reversibility Paradox, the notion of entropy, and the ontology of quantum mechanics are discussed. Other essays consider Humean supervenience and the question whether the physical world is deterministic.

In her new book Reconstructing Reality (henceforth RR), Margaret Morrison’s main target is the kind of information about the world (or, more specifically, about physical and biological systems) one can extract from the ‘reconstructive methods and practices of science’ (p. 1). To address this, Morrison focuses on three central kinds of interrelated strategies for ‘recasting nature’ (p. 2) by using reconstructive methods and practices: (i) abstract mathematical explanations and understanding (Part 1 of the book), (ii) scientific models (Part 2), and (iii) computer simulations (Part 3). Hence, RR is the ambitious attempt to connect and analyse three major topics in current philosophy of science.

Social epistemology is a relatively new and booming field of research. It studies the social dimension of the pursuit of acquiring true beliefs and requires philosophical as well as sociological and economic expertise. The insights gained in social epistemology are not only of theoretical interest; they also improve our understanding of social and political processes, as the field includes the analysis of group deliberation and group decision-making. However, surprisingly little work has so far been done on the epistemic properties of group deliberation, belief aggregation, and decision-making procedures. To close this gap, the construction and analysis of formal models are especially promising as formal modeling combines representational adequacy with instructive analytical results. This special issue collects papers that follow this strategy from the point of view of different disciplines.

One of the major problems that artificial intelligence needs to tackle is the combination of different and potentially conflicting sources of information. Examples are multi-sensor fusion, database integration and expert systems development. In this paper we are interested in the aggregation of propositional logic-based information, a problem recently addressed in the literature on information fusion. It has applications in multi-agent systems that aim at aggregating the distributed agent-based knowledge into an (ideally) unique set of propositions. We consider a group of autonomous agents who individually hold a logically consistent set of propositions. Each set of propositions represents an agent’s beliefs on issues on which the group has to make a collective decision. To make the collective decision, several aggregation procedures have been proposed in the literature. Assuming that all propositions in question are factually right or wrong, we ask how good belief fusion is as a truth tracker. Will it single out the true set of propositions? And how does information fusion compare with other aggregation procedures? We address these questions in a probabilistic framework and show that information fusion does especially well for agents with a middling competence of hitting the truth of an individual proposition.

In everyday life, as well as in science, we have to deal with and act on the basis of partial (i.e. incomplete, uncertain, or even inconsistent) information. This observation is the source of a broad research activity from which a number of competing approaches have arisen. There is some disagreement concerning the way in which partial or full ignorance is and should be handled. The most successful approaches include both quantitative aspects (by means of probability theory) and qualitative aspect (by means of graphical or causal models or logic). Some of these approaches have important impacts on various disciplines including philosophy, computer science, statistics, mathematics, physics, and social science. Most notably, the relation between causal and probabilistic information is a topic of interest in all of these fields.

Computer simulations have changed the face of many scientific disciplines. This has attracted the attention of a number of philosophers of science, who have started discussing the philosophical implications of the use of computational methods in science. It was the aim of the conference Models and Simulations that took place at the IHPST in Paris, France, on 12 and 13 June 2006 to bring researchers working in this field together and provide a platform to discuss these issues in a focused way. The papers in this special issue were presented at this conference. We would like to thank the IHPST and the CNRS (département SHS, ATIP “Physique et Calcul”) for generous financial support of the conference. We also would like to thank the authors and referees of the papers for their work, and Vincent Hendricks and John Symons for their support of the project of a special issue of this journal to the topic of the conference.

Modern science is, to a large extent, a model-building activity. But how are models contructed? How are they related to theories and data? How do they explain complex scientific phenomena, and which role do computer simulations play here? These questions have kept philosophers of science busy for many years, and much work has been done to identify modeling as the central activity of theoretical science. At the same time, these questions have been addressed by methodologically-minded scientists, albeit from a different point of view. While philosophers typically have an eye on general aspects of scientific modeling, scientists typically take their own science as the starting point and are often more concerned with specific methodological problems. There is, however, also much common ground in middle, where philosophers and scientists can engage in a productive dialogue, as the present volume demonstrates.